MAT337H1: Introduction to Real Analysis

Hours: 
36L

Construction of Real Numbers. Metric spaces; compactness and connectedness. Sequences and series of functions, power series; modes of convergence. Interchange of limiting processes; differentiation of integrals. Function spaces; Weierstrass approximation; Fourier series. Contraction mappings; existence and uniqueness of solutions of ordinary differential equations. Countability; Cantor set; Hausdorff dimension.

Prerequisite: 

MAT224H1/​MATB24H3/MAT224H5/ MAT247H1/​MAT247H5, MAT235Y1/​MAT235Y5/(MATB41H3, MATB42H3)/ MAT237Y1/​(MATB41H3, MATB42H3, MATB43H3)/MAT237Y5, MAT246H1; NOTE: These Prerequisites will be waived for students who have MAT257Y1

Exclusion: 

MAT357H1 & MAT378H5

Distribution Requirements: 
Science
Breadth Requirements: 
The Physical and Mathematical Universes (5)